Although mutation has chaotic aspects, spontaneous mutation rates assume certain characteristic values when expressed per genome per genome duplication. The rate among lytic RNA viruses is roughly 1, while the rate among retroelements is roughly 0.2. The rate among viral and cellular microbes with DNA chromosomes is close to 0.0034. Mutation rates among higher eukaryotes, estimated from specific-locus studies, vary greatly. Most of this variation can be suppressed if the rates are expressed per cell division instead of per sexual generation, and if the genome size is taken to be only a little larger than the sum of the protein-encoding sequences; then, the mutation rate is roughly 0.01. The reasons for different characteristic mutation rates among different organism groups remain mysterious and pose a substantial challenge to students of evolution.